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The aim of this paper is to propose a differential braking rollover mitigation strategy for wheeled vehicles. The strategy makes use of a polytopic (piecewise linear) description of the vehicle and includes translational and rotational dynamics, as well as suspension effects. The braking controller is robust and the system states are predicted to estimate the rollover risk up to a given time horizon. In contrast to existing works, the switched predictive nature of the control allows it to be applied only when risk of rollover is foreseen, interfering a minimum with driver's actions. The stability of the strategy is analyzed and its robustness is illustrated via numerical simulations using CarSim for a variety of vehicles. [ABSTRACT FROM AUTHOR]